
IHS: a variant of the HS, which models the problem of function minimization based on way musicians create their songs with optimal harmonies. This approach uses dynamic values for both the Harmony Memory Considering Rate (HMRC), which is responsible for creating new solutions based on previous experience of the music player, and the Pitch Adjusting Rate (PAR), which is in charge of applying some disruption to the solution created with HMRC in order to avoid the pitfalls of local optima. Both parameters are updated at each iteration with the new values within the range \([\) HMCR\(_{min},\) HMCR\(_{max}]\)  e \([\) PAR\(_{min},\) PAR\(_{max}]\) , respectively. Concerning PAR calculation, the bandwidth variable (bandwidth) \(\varrho \)  is used, and its values must be between \([\varrho _{min},\varrho _{max}]\) .

AIWPSO: a variant of the PSO, which considers any possible solution as a particle (agent) in a swarm. Each agent has a position and velocity vector in the search space, as well as two acceleration constants \(c_1\)  and \(c_2\) . A fitness value is associated with each position, and after some iterations the global best position is selected as the best solution to the problem. The AIWPSO is proposed to balance the global exploration and local exploitation abilities for PSO. For each iteration, every particle chooses an appropriate inertia weight along the search space by dynamically adjusting the inertia weight \(w\) .

CS: Cuckoo Search [1]}, [2]} employs a combination of the Lévy flight, which may be defined as a bird flight-inspired random walk with step \(\tau \)  over a Markov chain, together with a parasitic behavior of some cuckoo species. The model follows three basic ideas: i) each cuckoo lays one egg at a time in randomly chosen nests, ii) the host bird discover the cuckoo's egg with a probability \(p_a\in [0, 1]\)  and either discard the egg or abandon the chest and build a new one (a new solution is created), and iii) the nests with best eggs will carry over to the next generations.

FA: is derived from the fireflies' flash attractiveness when mating partners and attracting potential preys. Basically, the attractiveness \(\beta \)  of a firefly is computed by its position related to other fireflies in the swarm, as well as its brightness is determined by the value of the objective function at that position. Furthermore, the attractiveness depends on each firefly light absorption coefficient \(\gamma \) . In order to avoid local optima, the system is exposed to a random perturbation \(\alpha \) , and the best firefly performs a random walk across the search space.

BSA: it is a simple, effective and fast evolutionary algorithm developed to deal with problems characterized by slow computation and excessive sensitivity to control parameters. In a nutshell, it employs crossover and mutation operations together with a random selection of stored memories to generate a new population of individuals based on past experiences. BSA requires a proper selection of two parameters: the mixing rate (\(mix\_rate\) ), which controls the number of elements of individuals that will mutate in the population, as well as the \(F\)  parameter, which controls the amplitude of the search-direction matrix.

JADE: a differential evolution-based algorithm that implements the “DE/current-to-\(p\) -best" mutation strategy, which employs only the \(p\) -best agents in the mutation process. Additionally, JADE uses an optional archive for historical information, as well as an adaptive updating in the control parameter. JADE requires the selection of the parameter \(c\) , which stands for the rate of parameter adaptation, and \(g\)  (greedness), that determines the greediness of the mutation strategy.

CoBiDE: it also a differential evolution-based technique that employs a covariance matrix for a better representation of the system's coordinates during the crossover process. Additionally, mutation and crossover are controlled using a bimodal distribution to achieve a good trade-off between exploration and exploitation. The probability to execute the differential evolution according to the covariance matrix is defined by the parameter \(pb\) , as well as the proportion of individuals chosen from the current population to calculate the covariance matrix is denoted by \(ps\) .

